Small-spot spectrometry instrument with reduced polarization and multiple-element depolarizer therefor

ABSTRACT

A small-spot imaging, spectrometry instrument for measuring properties of a sample has a polarization-scrambling element, such as a birefringent plate depolarizer, incorporated between the polarization-introducing components of the system, such as the beamsplitter, and the microscope objective of the system. The plate depolarizer varies polarization with wavelength, and may be a Lyot depolarizer with two plates, or a depolarizer with more than two plates (such as a three-plate depolarizer). Sinusoidal perturbation in the resulting measured spectrum can be removed by data processing techniques or, if the depolarizer is thick or highly birefringent, the perturbation may be narrower than the wavelength resolution of the instrument.

PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.11/399,133 filed Apr. 6, 2006, now U.S. Pat. No. 7,158,229 which in turnwas a divisional of U.S. patent application Ser. No. 10/081,078, filedFeb. 21, 2002, now U.S. Pat. No. 7,099,081, which claims priority under35 U.S.C. 119(e) to U.S. Provisional Application No. 60/350,823, filedJan. 18, 2002, and wherein said U.S. patent application Ser. No.10/081,078 is a continuation-in-part of U.S. patent application Ser. No.09/932,548, filed Aug. 17, 2001, now U.S. Pat. No. 6,667,805, whichclaims priority under 35 U.S.C. 119(e) from prior U.S. ProvisionalApplication No. 60/226,396, filed Aug. 18, 2000.

TECHNICAL FIELD

The present invention relates generally to optical meteorology systemsthat measure optical characteristics of a sample in order to determinephysical properties of interest of the sample. Systems having opticalinstruments that measure light scattered from a sample (whether byreflection or transmission) and which interpret the measuredcharacteristics (e.g., by comparing with predictions of an opticalmodel) to determine physical parameters of the sample (e.g., ofgrating-like structures on a silicon wafer) are of particular relevance.Relevant optical instruments may include spectrometry instruments,spectroscopic reflectometers and transmissive spectrophotometers, andespecially those spectroscopy instruments which employ a microscopeobjective and associated imaging optical components for small-spotviewing of a sample having diffractive features to be measured.

The present invention relates especially to any optical meteorologysystems characterized by substantially unpolarized sample illuminationand by polarization-insensitive detection, so as to allow samples whoseoptical characteristics strongly depend on polarization (e.g., waferswith gratings) to be measured at arbitrary sample orientations relativeto the instrument. The invention also relates to improved depolarizerelements for such instruments.

BACKGROUND ART

Physical properties of a sample can be determined by interpretingmeasured optical characteristics of the sample. For example, the opticalcharacteristics may describe the light that has scattered from thesample, given the description of the light incident upon the sample.Physical properties of particular interest are parameters ofgrating-like structures on a silicon wafer. A reflectometer operating atnear normal incidence is one example of an optical instrument that canbe used to measure the properties of gratings on a wafer. In general,the interpretation mentioned above either implicitly or explicitlycompares measured light intensities to the predictions of an opticalmodel, which describes the incident light, the optical characteristicsof the sample, and the detection of light.

It is desirable in many situations to allow the wafer to be viewed atany rotational orientation upon its support. Allowance for arbitraryrotation of the sample is desired, for example, if the opticalinstrument is integrated into a process tool like a lithography track orpolishing tool for chemical mechanical polishing. A robot transportswafers (particular samples of interest) within the process tool tovarious process modules, and also delivers wafers to the meteorologysystem, which contains the optical instrument. The wafer is typicallyplaced on a flat support. The process tool as a whole may not besensitive to the specific rotation of the wafer at any point, and mayhave no provision for determining that orientation. Even if theorientation of the wafer is determined at some point in its processingpath through the process tool, the process modules or the robot may notmaintain this orientation. Since space is typically at a premium in sucha process tool, it is preferable to not need an independent “waferaligner” for the meteorology instrument.

The optical characteristics of grating-like structures have a markedsensitivity to the polarization of light. Samples with grating-likestructures will affect the amplitude and phase of the light they reflector transmit differently for different incident polarizations. The sameis also true for birefringent samples, or stacks of thin films at otherthan normal incidence. This can be an issue when making measurementswith some photometric instruments. In lithography applications, forexample, determining the linewidth or profile of diffractive patternfeatures formed on a semiconductor wafer or photomask may be performedby measuring the normal or near-normal incidence (hereafter collectivelyreferred to as quasi-normal incidence) reflectivity or other opticalproperties with a small-spot reflectometer or small-spot transmissivespectrophotometer. The spectral reflectivity or transmissivity of thesample being measured will depend to some extent on the degree ofpolarization of the incident light and on the orientation of the wafer.Thus, in order to allow arbitrary orientation of a grating sample whoseoptical characteristics depend strongly on polarization of the light,the illumination by the meteorology instrument must be effectivelyunpolarized. The detection by the instrument must likewise beinsensitive to polarization.

In some instruments it is possible to orient the sample so that thegrating-like structures of the pattern (or the optical axis of abirefringent surface or thin film stack) are presented in a known andconsistent direction relative to the instrument's incident light. Anysystematic errors due to polarization can then be minimized during dataprocessing. That is, by carefully characterizing the polarizationcharacteristics of the optics and modeling the effect on a sample'sresponse at a particular sample orientation relative to the polarizedlight, the measured data can be processed so as to eliminate thepolarization effect provided the sample is measured at the modeledorientation.

However, it is not always possible to provide a specified sampleorientation to the measuring instrument. Wafer handlers associated withlithography tracks frequently present the samples to the measuringinstrument in a consistent but unknown orientation that the measuringinstrument itself has no control over. Polishers produce a random sampleorientation. Hence, it would be preferable if the instrument'sillumination and collection optics were non-polarizing, so thatorienting the wafer would be unnecessary.

In the past, the effect of instrument polarization on measurementresults have been only a minor issue that has typically been ignoredexcept in those instruments where polarization itself is the parameterbeing measured. Polarimeters and ellipsometers deliberately use incidentlight of known polarization. Also, until recently, spectrometryinstruments were not used for measuring linewidth, profile, etc. ofgrating-like structures.

Unwanted polarization in the optics can be caused by polarizing elementssuch as tilted fold mirrors, beamsplitters, tilted glass surfaces,prisms, and spectrometer gratings. (In this context “polarizing” canmean partially polarizing or in some way affecting the polarizationstate.) One prior solution has been to reduce the polarization effect ofinstrument components by carefully arranging the planes of incidence ofthe tilted components in the system, so that for every such tiltedcomponent the instrument also has a similar component tilted in theperpendicular plane to cancel the polarization effect of the first. Thisuse of component pairs requires more room for the optics, so that itcannot be used when a compact system is needed. The pairing techniquecannot be used to alleviate the polarization effect in the spectrometercomponent of the system.

Depolarizers of several types are known. In Zeiss monolithicspectrometers, among others, light is coupled with a fiberoptic bundlethat scrambles the polarization. Fiber depolarizers cannot be used inthe imaging path because they would also scramble information about theimage. Wedge depolarizers, comprising a birefringent wedge plate and anindex-matched non-birefringent plate, need to be properly oriented tothe polarization of the light to be depolarized. Because they produce alaterally offset double image, they are not well suited for imagingsystems.

Lyot depolarizers, comprising two non-wedge-shaped birefringent plateswith their axes at 45° to each other, are commercially available, forexample from Karl Lambrecht and other optical component manufacturers.The basic element of a (plate) Lyot depolarizer, as shown in FIG. 1, isa birefringent plate 1 with “retardance” d. The retardance is given by

$\begin{matrix}{d = {{\frac{2\;\pi}{\lambda}\left( {n_{o} - n_{e}} \right)t} = {2\;\pi\;{{kf}.}}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$wherein λ is the wavelength in vacuum, t is the thickness of the plate,n_(o) is the optical index of the ordinary axis 3, n_(e) is the opticalindex of the extraordinary axis 5, k is the wavenumber (in vacuum), andf is the “retardance frequency”: the frequency (i.e., reciprocal period)of oscillations of the optical response of the plate as a function ofwavenumber,

$\begin{matrix}{k = \frac{2\;\pi}{\lambda}} & {{Eq}.\mspace{14mu} 2} \\{f = \frac{\left( {n_{o} - n_{e}} \right)t}{2\;\pi}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$(f is not strictly constant with respect to wavelength because n_(o) andn_(e) are typically wavelength-dependent, but the wavelength variationof f is typically much smaller than its magnitude.) Fiducial line 7 isfor illustrative purposes to indicate the position of the ordinary axis.The frequency of polarization variations induced by the plate isproportional to thickness of the plate and the difference betweenordinary and extraordinary indices.

As shown in FIG. 2, and described in U.S. Pat. No. 5,371,595, a Lyotdepolarizer 11 consists of two birefringent plates 13 and 15 withretardance frequencies in the ratio of 1:2, and with a relative rotation17 of 45° (π/4 radians) between their polarization axes. If the twoplates are of the same material, the thicknesses will also be in theratio of 1:2. The thinner plate will have the lower retardance frequencyf₀ corresponding to retardance d. The thicker will have retardancefrequency 2f₀ corresponding to retardance 2 d. The thinner plate istypically about 2 millimeters thick. Incident light 19 passing throughthe Lyot depolarizer 11 and emerging as transmitted light 21 has itspolarization scrambled in a wavelength-dependent manner.

Lyot depolarizers have previously been used in imagingspectroradiometers and spectropolarimeters for telescopes, for exampleon a satellite observing backscattered radiation from the earth tomonitor atmospheric ozone depletion. In contrast to fiber and wedgedepolarizers, Lyot depolarizers are image-preserving, and are thereforesuitable for imaging systems.

An object of the present invention is to provide a small-spotspectrometry instrument with pattern viewing capability for measuringgrating-like or other diffractive pattern structures on semiconductorwafers, photomasks, and the like, wherein the instrument's polarizationeffects on linewidth, profile, erosion and similar feature measurementsare minimized.

Another object of the present invention is to provide a depolarizer thatscrambles the polarization as a function of wavelength with improvedcharacteristics, e.g., over a Lyot depolarizer.

An additional object of the present invention is to provide aspectroscopy instrument that behaves as an ideal unpolarized instrumentthrough the use of such an improved depolarizer.

SUMMARY OF THE INVENTION

These objects have been met by a small-spot imaging, spectrometryinstrument in which an image-preserving, birefringent retardance platetype, polarization-scrambling element, such as a Lyot depolarizer or animproved three-plate depolarizer, is incorporated between thebeamsplitter and the microscope objective. The beamsplitter is the lastsignificant polarizing element in the illumination path prior to thesample. Preferably the polarization-scrambling element is placed in acollimated portion of the light path to avoid creating a double imageoffset in focus. When both the illuminating and collected light passthrough the same depolarizer, there is a preferred orientation for thedepolarizer.

The depolarizers used in this invention do not vary the polarizationspatially as wedge depolarizers do. Rather, they vary the polarizationwith wavelength. The sinusoidally perturbed spectrum that results can beremoved by data processing techniques. If the depolarizer is made thickenough or made from a highly birefringent material, such as calcite,alpha barium borate or quartz, then the sinusoidal perturbation may bemuch narrower than the wavelength resolution of the instrument. In thiscase the perturbation would not be detectable and no processing would berequired to remove it. The only disadvantage of using calcite for thedepolarizer material is that it does not transmit as much UV light asalpha barium borate or quartz. Disadvantages of alpha barium borate areits high cost, weaker birefringence, and sensitivity to humidity. Quartzhas even lower birefringence requiring very thick pieces to makeeffective depolarizers. The present invention is for an improveddepolarizer, which aids in achieving the goal of “unpolarized”illumination and detection in a normal incidence reflectometer. Itallows a sample, even one that changes the state of polarization oflight-upon reflection, to be measured at an arbitrary rotation.

The second and third objects of the invention have been met through theuse of an improved depolarizer that employs at least three birefringentplates. Each birefringent plate has a retardance (i.e., an induced phaseshift between two linear polarization modes). The plates are chosen withdifferent retardances, and they assembled with predetermined rotationsof their polarization axes with respect to one another and the opticalsystem. In a preferred embodiment, the three depolarizer plates arecomposed of the same material (e.g., calcite or crystalline quartz) andhave a thickness ratio of either 1:3:9 or 4:3:9 (depending on specificdesign requirements and constraints), although different materials canbe used and other thickness ratios can also work. The angles of theouter plates' polarization axes relative to the inner plate's axis arepreferably 45° and [cos⁻¹(−1/3)]/4=27.368°.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a birefringent retardance plate for usein a depolarizer.

FIG. 2 is a perspective view of a Lyot depolarizer, which usesretardance plates of the type shown in FIG. 1.

FIG. 3 is a schematic side plan view of a first embodiment of aspectrometry instrument according to the present invention, with a Lyotdepolarizer.

FIGS. 4 and 5 are schematic plan views of two alternate configurationsfor a spectrometry instrument according to the present invention, one aspectroscopic reflectometer with non-normal incidence and reflection andthe other a transmissive spectrophotometer.

FIG. 6 is a schematic side plan view of a second spectrometry instrumentaccording to the present invention, with an improved three-platedepolarizer.

FIG. 7 is a perspective view of a three-plate depolarizer of the presentinvention for use in a spectrometry instrument as in FIG. 6.

FIG. 8 is a graph illustrating relative polarization axis orientationsof the plates 202, 204 and 206 in the depolarizer of FIG. 7, where x andy represent polarization axis directions for plate 202.

FIG. 9 is a graph of the ordinary-extraordinary refractive indexanisotropy (n_(o)−n_(e)) versus wavelength for calcite and barium borate(BBO) retardance plate materials.

BEST MODE FOR CARRYING OUT THE INVENTION

With reference to FIG. 3, a spectrometry instrument 100 in accord withthe present invention, to detect reflectivity at a spot of interest onsample 128, is seen to include a Lyot depolarizer 122. The instrument100 in FIG. 3 is a near-normal incidence reflectometer. Illuminatinglight beam 104 from a light source (not shown) exits illumination fiber102. Turn mirror 106 deflects the illuminating light beam 104 throughcollimator 108. Turn mirrors 110 and 112 direct the light throughillumination aperture 114, and on to beam splitter 115. The beamsplitter 115 is preferably a plate beam splitter, rather than a cubebeamsplitter, to minimize ghost reflections. The beam splitter transmitsportion 116 of the illumination beam and beam dump 118 absorbs it.Alternatively, a reference spectrometer could be positioned in place ofbeam dump 118 to measure the transmitted portion 116. (Or, such areference spectrometer might be positioned instead to receive lighttemporarily diverted from path 120 via a flip-in mirror or other beamswitch.) Portion 120 of the illumination reflects off beam splitter 115and propagates through depolarizer 122, objective 124 and window 126, toultimately illuminate wafer 128.

A window 126 physically isolates the wafer 128 from the meteorologyinstrument 100 and any associated contaminant risk, while still allowingthe wafer features to be optically measured. The wafer 128 sits on asupport 162 which may be used to move or rotate the wafer under theinstrument 100 to one or more specified test positions, as representedby the rotation axis θ. The spectrometry instrument's optics may bemounted to a back plane capable of translating in a lateral direction yrelative to the wafer support 162. Focusing motion in a longitudinaldirection z may be performed either by moving the objective 124 orsample support 162 or both. A wide area camera system (not shown) mightalso be provided in addition to CCD camera 152 to locate the generalarea of interest for measurement by the instrument 100.

Wafer 128 reflects a portion of illumination beam 120 as reflected beam130, which propagates back to beam splitter 115 via window 126,objective 124 and Lyot depolarizer 122. (For convenience, theillumination and reflected beams 120 and 130 are shown separately inFIG. 3. In practice the beams substantially overlap, although thereflected beam 130 will have different spectral and spatialcharacteristics.) The portion of reflected beam 130 that is reflected bybeamsplitter back towards illumination fiber 106 is ignored. Portion 132of reflected beam 130 passes through the beam splitter and proceedsthrough detection aperture 134 and imaging optic 136, via turn mirror138, to be focused on pin-hole mirror 140. Pin-hole mirror 140 passes asample of reflected beam 132 through to spectrometer fiber 142 whichdirects it to spectrometer 144. Pin-hole mirror 140 reflects theremainder of beam 132 back through re-imaging optic 148 to CCD camera152 via turn mirrors 146 and 150.

Collimator 108 collects the diverging rays exiting illumination fiber102 as illumination beam 104. The collimator 108 forms an image of thefiber to provide Kohler illumination for the objective 124. Collimator108, as well as objective 124, imaging optic 136 and re-imaging optic148 may consist of multiple elements, as is well known in the art. Theturn mirrors 110, 112, 138, etc. are for convenience and compactness ofpackaging. Aperture 114 controls the numerical aperture of beam 120 whenit illuminates wafer 128. This is important to prevent vignetting,control the range of incidence angles of light 120 upon wafer 128, asare well known in the art. The depolarizer 122 is preferably oriented ata slight angle to avoid unwanted reflections back along the principallight path. Also, the light between the beamsplitter 115 and thedepolarizer 122 is preferably collimated to minimize aberrations. Theoptics from the illumination source (not shown) through beam splittercan have polarization effects on 120, so that it is typically notunpolarized. Depolarizer 122 will be discussed in some detail below.Objective 124 collects illumination 120 and focuses it on wafer 128, andthen collects and collimates reflected light 130. Beam splitter 115allows illumination beam 120 and reflected beam 130, which is to bedetected, to overlap in space. This facilitates behavior as a normalincidence reflectometer. Beam dump 118 is reduces the stray light in theinstrument, to improve its accuracy. Detection aperture 134 limits thedetection of reflected angles to the detection numerical aperture, mayexclude unwanted diffracted orders, and controls the diffraction spotsize of the detection system and imaging system, as are well known inthe art. Preferably, illumination aperture 114 is larger than detectionaperture 134, to produce an overfilled instrument, to limit sensitivity,for example, to tilt of wafer 128. Imaging optic 136 creates an image ofthe wafer at pin-hole mirror 140. This allows the pinhole to pass aportion of light that has reflected from a well defined spot on thewafer to be detected by spectrometer 144. The pin-hole mirror reflectsthe rest of reflected beam 132 (that has not passed through the pinhole)so that re-imaging optic 148 can produce an image of the wafer on CCDcamera 152. This image will be missing the spot of light that has passedthrough pinhole mirror 140 and has been detected by spectrometer 144.This dark spot on the camera image of wafer 128 indicates exact locationof the measurement spot with respect to features on the wafer.

With reference to FIGS. 4 and 5, the spectrometry instrument need not bea normal-incidence reflectometer as in FIG. 3, but could be modified fornear normal spectroscopic reflectometry or for transmissionspectroscopy. In each case, polarization can be varied with opticalfrequency by inserting Lyot depolarizers in the light paths. In FIG. 4,a non-normal incidence spectroscopic reflectometer differs from thespectroscopic reflectometer of FIG. 3 by having separate illuminationand reflected light paths with a pair of microscopic objectives 37 and43 and at least one and possibly two depolarizing elements 35 and/or 45.Illumination optics 31, corresponding for example to the optical fiber102, condensing lens 108 and fold mirrors 106, 110 and 112 in FIG. 3,provide light 33 that is directed through a first Lyot depolarizer 35and this focused by a microscope objective 37 to a small spot 39 on asample 40. Light 41 reflected from the sample 40 is gathered by a secondmicroscope objective 43, passed through a second Lyot depolarizer 45 tocollection optics 47, corresponding for example to the elements 134-144in FIG. 3 and including a spectrometer component like element 144 ofFIG. 3. In FIG. 5, a transmissive spectrometry instrument fortransmission samples 60 also has pairs of depolarizers 55 and 65 andmicroscope objectives 57 and 63 in separate illumination and collectionlight paths, which are located on opposite sides of the sample location.Illumination optics 51 provide light 53 whose polarization is variedwith wavelength by the Lyot depolarizer 55, which is then focused by amicroscope objective 57 to a spot 59 on the sample 60. Light 61transmitted through the sample 60 is collected by objective 63, againdepolarized 65 and sent to collection optics 67 that includes aspectrometer. One or more of the microscope objectives in any of theembodiments could be catadioptric, that is include mirror elements, inwhich case there may be some advantage to placing the depolarizersbetween the objective and sample location even though that positioningmay increase chromatic aberration. Also, if either the illuminationoptics 31 or 51 or the collection optics 47 or 67 are such that they donot significantly polarize the light, then the depolarizer 35, 45, 55 or65 could be removed from that path.

Alternatively, the spectrometer could be replaced with a photodetectorand the light source could be a scanning monochromator. In this case,each wavelength band is measured sequentially.

The effect of polarizing elements and depolarizers on light, andultimately on measurements, is a complex physical phenomenon that may bemodeled in a number of different manners. A typical method is the use ofStokes parameters to describe the polarization of light, and Muellermatrices to describe the effect of optical elements on the light. Theseare described, for example in Chapter 2 of The Handbook of Optics, Vol.2, 2nd Edition (Michael Bass, editor, 1995). Also see “Ellipsometry andPolarized Light,” Azzan and Bashara, 1987.) Light of arbitrarypolarization and wavelength is described by the Stokes vector:

$\begin{matrix}\begin{pmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{pmatrix} & {{Eq}.\mspace{14mu} 4}\end{matrix}$S₀ is the total intensity of the light, and the S₁, S₂, and S₃ aredifferences of intensities for different polarizations. Unpolarizedlight has the Stokes vector

$\begin{matrix}{\begin{pmatrix}S_{0} \\0 \\0 \\0\end{pmatrix}.} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

The values of the Stokes vector depend on the orientation of itscoordinate system. The coordinate system can be rotated (mathematically)by an angle of p with a rotation Mueller matrix

$\begin{matrix}{{R(p)} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\cos\left( {2p} \right)} & {- {\sin\left( {2p} \right)}} & 0 \\0 & {\sin\left( {2p} \right)} & {\cos\left( {2p} \right)} & 0 \\0 & 0 & 0 & 1\end{bmatrix}.}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

As noted in the background art section above, the basic element of a(plate) Lyot depolarizer, as shown in FIG. 1, is a birefringent plate 1with “retardance” d. The retardance is given by

$\begin{matrix}{d = {{\frac{2\;\pi}{\lambda}\left( {n_{o} - n_{e}} \right)t} = {2\;\pi\;{{kf}.}}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$wherein λ is the wavelength in vacuum, t is the thickness of the plate,n_(o) is the optical index of the ordinary axis 3, n_(e) is the opticalindex of the extraordinary axis 5, k is the wavenumber (in vacuum), andf is the “retardance frequency”: the frequency (i.e., reciprocal period)of oscillations of the optical response of the plate as a function ofwavenumber,

$\begin{matrix}{k = \frac{2\;\pi}{\lambda}} & {{Eq}.\mspace{14mu} 2} \\{f = \frac{\left( {n_{o} - n_{e}} \right)t}{2\;\pi}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$(f is not strictly constant with respect to wavelength because n₀ andn_(e) are typically wavelength-dependent, but the wavelength variationof f is typically much smaller than its magnitude.) Fiducial line 7 isfor illustrative purposes to indicate the position of the ordinary axis.The frequency of polarization variations induced by the plate isproportional to thickness of the plate and the difference betweenordinary and extraordinary indices. The Mueller matrix for the platewith its ordinary axis along the x-axis is

$\begin{matrix}{{D(d)} = {\begin{pmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & {\cos\; d} & {\sin\; d} \\0 & 0 & {{- \sin}\; d} & {\cos\; d}\end{pmatrix}.}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$The Mueller matrix M(p) for a birefringent plate that has been rotatedby an angle p is the original (unrotated) Mueller matrix pre- andpost-multiplied by two rotation matrices:M(p)=R(p)M(0)R(−p).  Eq. 8wherein M(0)=D(d), as defined in Eq. 7.

As shown in FIG. 2, a commercially available Lyot depolarizer consistsof two birefringent plates 13 and 15 with retardance frequencies in theratio of 1:2, and with a relative rotation 17 of 45° (π/4 radians)between their polarization axes. The plates 13 and 15 may be composed ofany of a variety of available birefringent crystal materials, such asquartz, calcite, or alpha barium borate (BBO). If the two plates are ofthe same material, the thicknesses will also be in the ratio of 1:2. Thethinner plate will have the lower retardance frequency f₀ correspondingto retardance d. The thicker will have retardance frequency 2f₀corresponding to retardance 2 d. The thinner plate is typically about 2millimeters thick.

Each depolarizer plate material has unique characteristics that shouldbe considered when selecting a depolarizer. Calcite does not transmit asmuch UV light as alpha barium borate or quartz. Alpha barium borate hasweaker birefringence than calcite, is sensitive to humidity, and isexpensive. Quartz has even lower birefringence requiring very thickpieces to make effective depolarizers, but transmits UV light very well.

The plates have a retardance that is strongly dependent on wavelength,so this type of depolarizer periodically varies the polarization versusthe light's optical frequency. The polarization introduced by the restof the optics in the meteorology instrument then produces a sinusoidalripple on the measured spectrum. The period of this sinusoidalperturbation is nearly constant in terms of wavenumber, so if the datais averaged over intervals equal to integer multiples of the rippleperiod, the effect of the sinusoidal variation and thus of theinstrument polarization is eliminated. Another way that the sinusoidalripple effect can be mathematically eliminated during data processing isto regress to find the best-fit theoretical spectrum to the sinusoidallyperturbed data assuming an ideal depolarizer. The best theoreticalspectrum will naturally follow the middle of the perturbed spectrum. Theperturbations may not be evident, and no processing would be required toremove it, if the depolarizer is thick enough and/or made with a highlybirefringent material. In that case, the sinusoidal perturbation may bemuch narrower than the wavelength resolution of the instrument.

A model for a Lyot depolarizer takes incident light 17 having anarbitrary Stokes vector S_(in) (i.e., with an arbitrary state ofpolarization) and yields the Stokes vector S_(out), for transmittedlight 19:

$\begin{matrix}{S_{out} = {{R\left( {\pi/4} \right)}{D\left( {2d} \right)}{R\left( {{- \pi}/4} \right)}{D(d)}S_{i\; n}}} & {{Eq}.\mspace{14mu} 9} \\{S_{out} = {\begin{bmatrix}S_{0} \\\begin{matrix}{\;{\frac{1}{\; 2}\;\left\{ {{{+ \; S_{\; 1}}\; 2\;\cos\; 2\; d}\; + \;{S_{\; 2}\left\lbrack {{\cos\; d}\; - \;{\cos\; 3\; d}} \right\rbrack}\; -}\; \right.}} \\\left. {S\;{3\left\lbrack {{\sin\; d}\; + \;{\sin\; 3d}} \right\rbrack}} \right\}\end{matrix} \\{{S_{2}\cos\; d} + {S\; 3\;\sin\; d}} \\\begin{matrix}{\;{\frac{1}{\; 2}\;\left\{ {{{+ \; S_{\; 1}}\; 2\;\sin\; 2\; d}\; + \;{S_{\; 2}\left\lbrack {{\sin\; d}\; - \;{\sin\; 3\; d}} \right\rbrack}\; -}\; \right.}} \\\left. {S\;{3\left\lbrack {{\cos\; d}\; + \;{\cos\; 3d}} \right\rbrack}} \right\}\end{matrix}\end{bmatrix}.}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$The goal is to have S_(out) unpolarized (Eq. 5). Notice the termsdesired to be zero have wavelength-dependent retardances with retardancefrequencies of 1, 2 and 3 times the retardance frequency of the thinnerof the two plates. If the detection system averages over one or moreperiods of the lowest retardance frequency the wavenumber-averagedoutput Stokes vector <S_(out)> is exactly what is desired:

$\begin{matrix}{{\left\langle S_{out} \right\rangle = \begin{bmatrix}S_{0} \\0 \\0 \\0\end{bmatrix}},} & {{Eq}.\mspace{14mu} 11}\end{matrix}$i.e., the transmitted light 19 would be effectively depolarized.Typically, a system would not average over an exact integer number ofperiods of the lowest retardance frequency, but would rather beintegrated over some “window” of wavenumbers with a tapered integrationweighting function. The spectral width of the weighting function definesthe optical system's spectral resolution or “bandwidth”. In general, theeffective optical response of such a system will tend to approach Eq. 11as either the system's spectral bandwidth width becomes large or thefundamental retardance frequency f₀ becomes large.

The “depolarization” achieved in this way is “effective” depolarization,not true depolarization. In other words, while individual wavenumbersmay be at least partially polarized, a “reasonable” average overwavenumber will not be polarized. Assuming that the rapid polarizationvariations induced by the Lyot depolarizer do not interact in acorrelated manner with similar rapid variations induced by otherelements in the optical system, the Lyot depolarizer works well.

There are other possible designs for a polarization-scrambling element.For example, more than two plates can be used and different combinationsof axes orientation or thickness can be used with nearly the sameperformance. A single plate can even be used if its optical axis is keptat 45° to the polarizing direction of the sample. Any of thesealternative designs can be use in place of, or in combination with, aLyot depolarizer.

The polarization can also be effectively scrambled by varying thepolarization state with time and averaging a detector signal over time.For example, the polarization state can be varied by rotating an opticalelement between the sample and other polarizing optics, as the signal isdetected.

When the illumination and reflected light pass through the samedepolarizer as is shown in FIG. 3, some sensitivity to the sample'srotational orientation occurs that varies only slowly with wavelength.This effect can be minimized by orienting the depolarizer so the thinplate is facing the wafer and the optical axis of the thicker plate isparallel to the plane of incidence on beamsplitter 115. This effect canalso be minimized by covering part of the aperture of objective 124 witha depolarizer of a different thickness or orientation, but this willdegrade the image quality slightly.

However, two Lyot depolarizers in series can lead to problems as thesecond depolarizer also varies the polarization rapidly. Consider thecase of using instrument 100 in FIG. 3 with Lyot depolarizer 122 todetect reflectivity at a spot of interest on sample 128. That theillumination and the reflection from the wafer pass through the samedepolarizer is equivalent to using two identical depolarizers in seriesin a transmission experiment. Depolarizer 122 has several desiredfunctions and properties. It should allow good imaging of the wafersurface on pinhole mirror 140, for good spot size, and onto CCD camera152. It should allow the wafer to rotate without changing the detectedintensity reflected from the spot. In order for this to be true, thelight illuminating the wafer should be effectively depolarized, and thelight reflected back through the depolarizer should also be effectivelydepolarized. Since the properties of the rest of the optical system, forexample, the beam splitter will cause polarization of the incidentlight, or polarization sensitivity of the detection, the depolarizer isresponsible for effectively depolarizing both the illumination anddetection. Finally, the spectrometer signal, the goal of detection, willbe compared to some model of optical properties of the wafer andinstrument. It is preferable that the optical characteristics of thesample and instrument affecting the spectrometer signal are as easy tomodel as possible.

The signal response (sig) of an optical system containing an opticalsubsystem with Mueller matrix M issig=S_(D)M S₁  Eq. 12wherein S₁, is a 4-by-1 Stokes vector that characterizes theillumination source and optics between the source and the subsystem, andS_(D) is a 1-by-4 “conjugate Stokes vector” that characterizes theoptical detector and optics between the subsystem and the detector,

$\begin{matrix}{{S_{I} = \begin{bmatrix}S_{I\; 0} \\S_{I\; 1} \\S_{I\; 2} \\S_{I\; 3}\end{bmatrix}},{S_{D} = \left\lbrack {S_{D\; 0}\mspace{14mu} S_{D\; 1}\mspace{14mu} S_{D\; 2}\mspace{14mu} S_{D\; 3}} \right\rbrack}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$For many cases of practical interest the polarization effects of theinstrument have a form that is simpler than the most general case of Eq.12. Typically, the illumination and collection optics have orthogonallinear polarization modes (i.e. polarization states that are unaffectedby the optics), in which case the last two components of both S₁ andS_(D) vanish (when referenced to the optical system's natural coordinateframe),

$\begin{matrix}{{S_{I} = \begin{bmatrix}S_{I\; 0} \\S_{I\; 1} \\0 \\0\end{bmatrix}},{S_{D} = \left\lbrack {S_{D\; 0}\mspace{14mu} S_{D\; 1}\mspace{14mu} 0\mspace{14mu} 0} \right\rbrack}} & {{Eq}.\mspace{14mu} 14}\end{matrix}$For an instrument like that shown in FIG. 3 this is expected. (This isthe case when the only significantly polarizing elements in theillumination and collection optics are mirrors, and the incidence planesof adjacent mirrors are either parallel or orthogonal.)

For the present discussion, the optical “subsystem” characterized by Mcomprises the measurement sample 128, depolarizer 122, and anyintervening optics (e.g. objective lens 124). Typically, the interveningoptics are not significantly polarizing, and their effect be neglectedin the following discussion. For many cases of practical interest, thesample has orthogonal linear polarization modes, and its Mueller matrixM_(S) (referenced to the sample's natural coordinate frame) has the form

$\begin{matrix}{M_{S} = {\begin{bmatrix}R_{0} & R_{1} & 0 & 0 \\R_{1} & R_{0} & 0 & 0 \\0 & 0 & R_{2} & R_{3} \\0 & 0 & {- R_{3}} & R_{2}\end{bmatrix}.}} & {{Eq}.\mspace{14mu} 15}\end{matrix}$This must be pre- and post-multiplied by Mueller rotation matrices (Eq.6) to account for the sample's rotational alignment; thus in the absenceof the depolarizer the subsystem Mueller matrix M isM=R(p)M _(S) R(−p).  Eq. 16The detector signal, for no depolarizer, is algebraically

$\begin{matrix}{{sig} = {{S_{D\; 0}R_{0}S_{I\; 0}} + \frac{{S_{D\; 1}\left( {R_{0} + R_{2}} \right)}S_{I\; 1}}{2} + {\cos\; 2{q\left( {{S_{D\; 1}S_{I\; 0}} + {S_{D\; 0}S_{I\; 1}}} \right)}R_{1}} + {\frac{\cos\; 4q}{2}S_{D\; 1}{S_{I\; 1}\left( {R_{0} + R_{2}} \right)}}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$(from Eq's. 6, 12, 14, 15, 16).

With no depolarizer, the detector signal has several undesirableproperties. It depends on rotation of the wafer. This either must beaccounted for mechanically by ensuring that the wafer is always orientedwith respect to optical instrument 100, or mathematically by knowing qand various additional quantities, as shown in the equation. Otherwise,there will be a measurement error introduced by the wafer's rotation.The detector signal depends not only on the wafer's total reflectivityR₀, but also on polarization characteristics R₁ and R₂. Again, to avoiderrors, these could be accounted for mathematically, with significanteffort. Finally, there are several products of illumination anddetection characteristics (the S terms) which must be calibrated or theywill cause errors.

Calibration means that special samples with known properties aremeasured on the instrument, and one or more properties of the instrumentare determined. Typically these calibration properties of the instrumentare stored and used for the interpretation of later measurements.

If the instrument were ideal in the sense that S_(l1) and S_(D1) werezero (in addition to the other zeros implicit in Eq. 14), SO thatillumination and detection had no polarization, Eq. 17 reduces tosig=(S _(D0) S _(l0))R ₀  Eq. 18where there is only one product, S_(D0)S_(l0), that needs to becalibrated, no rotation sensitivity, and only one property of the wafer(R₀) to be handled mathematically.

With a Lyot depolarizer, the wafer-depolarizer subsystem described abovehas a Mueller matrix M given byM=D(d)R(π/4)D(2d)R(p)M _(S) R(−p)D(2d)R(−π4)D(d).  Eq. 19(This assumes that the thinner depolarizer plate is furthest from thewafer and is aligned to the instrument's polarization axes. p is theangle between the wafer's and the thicker plate's polarization axes.)The final results of the reflectometer with a Lyot depolarizer and thesample described above is

$\begin{matrix}{{sig} = {{S_{D\; 0}R_{0}S_{I\; 0}} + {S_{D\; 1}{S_{I\; 1}\left\lbrack {\frac{\left( {R_{0} + R_{2}} \right)}{4} + {\cos\; 2d\frac{\left( {R_{0} + {3R_{2}}} \right)}{4}}} \right\rbrack}} - {S_{D\; 1}R_{3}S_{I\; 1}\sin\; 2d\;\cos\; 2q} - {\left( {{S_{D\; 1}S_{I\; 0}} + {S_{D\; 0}S_{I\; 1}}} \right)R_{1}\cos\; d\;\sin\; 2q} + {\frac{S_{D\; 1}S_{I\; 0}}{4}\left( {{- R_{0}} + R_{2}} \right)\left( {1 + {\cos\; d}} \right)\cos\; 4q}}} & {{Eq}.\mspace{14mu} 20}\end{matrix}$If the detector effectively integrates over wavelength to cancel out theretardance oscillations of the Lyot depolarizer, the trig functionscontaining d average out to zero and the resulting spectrally-averagedsignal <sig> is

$\begin{matrix}{\left\langle {sig} \right\rangle = {{S_{D\; 0}R_{0}S_{I\; 0}} + {S_{D\; 1}S_{I\; 1}\frac{\left( {R_{0} + R_{2}} \right)}{4}} + {\frac{S_{D\; 1}S_{I\; 0}}{4}\left( {{- R_{0}} + R_{2}} \right)\cos\; 4q}}} & {{Eq}.\mspace{14mu} 21}\end{matrix}$While this result with the Lyot depolarizer and adequate averaging isbetter than for the instrument with no depolarizer it does not yield thedesired result shown in Eq. 18 for an ideal reflectometer. Thisindicates, as mentioned above, that a Lyot depolarizer operating indouble-pass mode does not effectively depolarize light that passesthrough it, in the manner that a single-pass depolarizer does. A betterdepolarizer is required to achieve the desired results equivalent to aninstrument with no polarization sensitivity.

FIG. 6 shows a preferred embodiment of the instrument. It is verysimilar to the prior-art instrument shown in FIG. 3, so only differencesand specific preferred aspects will be highlighted here. (Referencenumerals in FIG. 6 are incremented by 100 relative to the correspondingelements in FIG. 3.) Again, the preferred light source (not shown)supplies light to fiber 202 with visible and UV light. Like beamsplitter115, beamsplitter 215 is preferably a plate beamsplitter rather than acube beamsplitter to avoid ghost reflections and degradation of thecement in UV light. In FIG. 6, the depolarizer 222 preferably consistsof three plates with the relations discussed below. Like depolarizer122, it is preferably oriented at a slight tilt angle to avoid multiplereflections between the depolarizer and the sample. Again, the lightbetween the beamsplitter 215 and depolarizer 222 should preferably becollimated to minimize optical aberrations.

Preferably optics in group 260 are mounted together to allow motion yalong a radius of wafer 228, and support 262 allows rotation θ of wafer228 about the z axis, giving the instrument the capability to scan itsspot over the wafer in a polar coordinate system. Focusing motion in alongitudinal (z) direction may be performed either by moving theobjective 224 or sample support 262 or both. Many alternativeembodiments are possible to allow scanning of the wafer.

A preferred embodiment of a depolarizer is shown in FIG. 7. Thisdepolarizer 71 has three plates 73, 74 and 75, with thicknesses in theratios of 4:3:9, respectively. (Plate 75 is closest to the wafer.) Forexample thicknesses of 1.5, 1.125 and 3.375 mm, respectively. Theoptical axes of the plates are typically parallel to the flat surfaces.Fiducial 77 marks the direction (i.e., the rotation normal to the zaxis) of one of the polarization axes of plate 73 (either the ordinaryor extraordinary axis). Plate 74 has one of its polarization axesindicated by fiducial 78 and rotated by angle α₁, from the polarizationaxis of plate 73. Angle α₁, is preferably equal to 45°, as indicated inFIG. 8. Plate 75 has its polarization axis indicated by fiducial 79,which is rotated by α₂≈27.368° from the polarization axis of plate 74.

As indicated in the discussion above, the plates in depolarizer 71 areanisotropic with well-defined polarization axes. The preferreddepolarizer has plates 73-75 of calcite. The anisotropy of calcite canbe characterized as the difference between the ordinary andextraordinary optical indices (n_(o)−_(e)), which are themselvesfunctions of wavelength, as shown in FIG. 9. An alternative material isBBO (Barium Borate). It has a lower anisotropy, as shown in FIG. 9, sothe plates for equivalent depolarization must be thicker, as discussedbelow. Another disadvantage is it is hygroscopic, i.e., it absorbswater. One advantage of BBO is lower absorption of especially UVwavelengths.

Generalizing from Eq. 19, the wafer-depolarizer subsystem with theabove-described 3-plate depolarizer substituted for the Lyot depolarizerhas a Mueller matrix M given byM=D(d ₁)R(a ₁)D(d ₂)R(−a ₂)D(d ₃)R(p)M _(S) R(−p) ×D(d ₃)R(−a ₂)D(d₂)R(−a₁)D(d ₁)  Eq. 22wherein d₁, d₂ and d₃ are the retardances of plates 73, 74 and 75,respectively. Upon expanding this expression and applying atrigonometric reduction to the retardance factors, it is evident thatEq. 22 reduces to a linear combination of trigonometric terms of theformcos(m₁d₁+m₂d₂+m₃d₃), sin(m₁d_(1+m) ₂d₂+m₃d₃)  Eq. 23wherein m₁, m₂ and m₃ are integers in the rangem₁,m₂,m₃=0,±1,±2  Eq. 24Each such trigonometric argument (m₁,d_(1+m) ₂d₂+m₃d₃) defines anassociated retardance frequency

$\begin{matrix}{f = {\frac{\left( {n_{o} - n_{e}} \right)}{2\;\pi}\left( {{m_{1}t_{1}} + {m_{2}t_{2}} + {m_{3}t_{3}}} \right)}} & {{Eq}.\mspace{14mu} 25}\end{matrix}$wherein t₁, t₂ and t₃ are the thicknesses of plates 73, 74 and 75,respectively, cf. Eq. 1. (It is assumed here that the three plates arecomposed of the same material, which is characterized by ordinary andextraordinary refractive indices n_(o) and n_(e).) The smallest suchretardance frequency (excluding the trivial case, m_(1,=m) ₂=m₃=0)defines a “fundamental retardance frequency” f_(o). Under the assumptionthat f_(o) is sufficiently large that polarization variations of thisfrequency are not resolvable by the instrument, all of the trigonometricfunctions of retardance (terms of the form indicated in Eq. 23) averageout to zero in the spectrally-averaged signal. The resulting signalcontains retardance-independent terms that are dependent on the wafer'srotation angle p and polarization properties; however this dependencecan be eliminated by choosing appropriate alignment angles a₁ and a₂between the plates. The angles that satisfy this criterion are

$\begin{matrix}{a_{1} = {\frac{\pi}{4} + {j_{1}\frac{\pi}{2}}}} & {{Eq}.\mspace{14mu} 26} \\{a_{2} = {{{\pm {arc}}\;{{\cos\left( {{- 1}/3} \right)}/4}} + {j_{2}\frac{\pi}{2}}}} & {{Eq}.\mspace{14mu} 27}\end{matrix}$wherein j₁, and j₂ are arbitrary integers. For the situation where thereis adequate averaging over wavelength, this yields thespectrally-averaged signal <sig>,

$\begin{matrix}{\left\langle {sig} \right\rangle = {\left( {{S_{D\; 0}S_{I\; 0}} + \frac{S_{D\; 1}S_{I\; 1}}{3}} \right)R_{0}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$This is the desired result, as there is no dependence on wafer rotation,one collection of terms S_(D0)S_(l0)+S_(D1)S_(l1)/3 which is requiredfor calibration at each wavelength, and only one property of the waferfor calculation, R₀.

The above result is based on Eq's. 12, 13 and 22—it does not assume themore restrictive form Eq. 14 for S_(l) and S_(D). Thus the operation ofthe device does not depend on special symmetries of the optical system'spolarization properties, and in this mode of operation its performancedoes not depend on the depolarizer's rotational orientation. Althoughthe above result only applies to a sample having a Mueller matrix M_(S)having the form of Eq. 15, the result extends partially to the moregeneral case: For an arbitrary sample Mueller matrix M_(S), <sig>remains insensitive to sample rotation, although it does exhibit somesensitivity to the sample's polarization characteristics.

A key assumption of the above analysis is that the fundamentalretardance frequency f_(o) is sufficiently large that thedepolarizer-induced polarization variations are not detectable. The goalis to maximize f_(o), subject to practical constraints. As an example,consider the case when the response of one pixel of detector 252 has aGaussian response so its signal output<sig>=e∫I(k)exp[−((k−k ₀)/(cw))² ]dk.  Eq. 29is an integral over wavenumber of the product of the intensity spectrumI(k) and a Gaussian function with a full width, half maximum value of wand center wavenumber k₀. c is a constant (˜0.6), and e is a constantincluding the detector efficiency. I(k) is a linear superposition ofterms of the form cos(2πf), sin(2πf), with f being a retardancefrequency defined by Eq. 25. The integral of Eq. 29 comprises a linearcombination of corresponding terms of the form

$\begin{matrix}{v_{z} = {\frac{I_{z}e}{\sqrt{\pi}\; c\; w}{{\exp\left\lbrack {- \left( {\pi\; f\; c\; w} \right)^{2}} \right\rbrack}\;.}}} & {{Eq}.\mspace{14mu} 30}\end{matrix}$Note that the amplitude of such a term decreases rapidly, as a squaredinverse exponential, as the retardance frequency f increases, or as thefull-width, half-max bandwidth w of the detector increases. Thebandwidth of a detector pixel has other requirements placed upon it, forexample, it must adequately resolve the sample-induced signal variationswith wavenumber. Therefore it is not desirable to make w as wide asmight be necessary to obtain good averaging. For a given detectorbandwidth, then, it is desirable to have the largest fundamentalretardance frequency f_(o) resulting from the sums in Eq. 25. Theexample in Eqs. 29 and 30 assumed a Gaussian form for a detectorsresponse, a common assumption. Similar conclusions would be drawn fromother detector response functions.

Increasing the thicknesses of the plates in proportion can alwaysincrease the minimum frequency. However, there are other practicallimitations on total thickness. One limitation can be absorption in theplates, especially, e.g., in the UV range. Another limitation may besimply size, or cost of the raw material. One solution is to choose thethickness in the ratios of 1:3:9. This is optimal in the sense that, fora given total combined thickness, it yields the highest fundamentalfrequency f_(o). A preferred solution may be to choose the thicknessesin the ratios of 4:3:9 so that the thinnest plate is thicker and easierto fabricate and assemble. For the 1:3:9 designf_(o)=(n_(o)−n_(e))T/(26π), wherein T is the total plate thickness(T=t₁+t₂+t₃), whereas the 4:3:9 design yieldsf_(o)=(n_(o)−n_(e))T/(32π).

The performance limitation imposed by the fundamental frequency f_(o)can be partially circumvented if the optical system satisfies symmetryproperties implicit in Eq. 14. For this case, the signal depends only onthe four Mueller matrix elements in the first quadrant of M (i.e., thefirst two rows and columns of M). By choosing the order of thedepolarizer plate thicknesses and angles and the orientation of thedepolarizer, one or more of the lowest retardance frequencies can bemade to vanish in the first quadrant. For both the 1:3:9 and 4:3:9,there are several orderings for which the two lowest frequencies vanish.The 4:3:9 design also has a configuration for which the three lowestfrequencies vanish. In this configuration, the thickest plate is in themiddle, the thinnest plate is furthest from the wafer, and the anglebetween the thickest and thinnest plates' polarization axes is 45°. (Thepolarization axis of the plate furthest from the wafer should be alignedto the instrument's polarization axis.)

As mentioned above, scaling the thicknesses for a given ratio to thickervalues gives better averaging properties to achieve effectivedepolarization, however, it may lead to excessive UV absorption. Thepreferred thicknesses to balance this tradeoff have a sum of 6 mm: 0.5mm, 1.125 mm, and 3.375 mm respectively for plates 73, 74 and 75.

Instrument 200, used for illustrative purposes, is a reflectometer. Fora true normal-incidence reflectometer, it is necessary to have onedepolarizer in the location shown, through which pass both illuminatingand detected light. Such an instrument is necessarily implemented with abeam splitter, which typically has polarization effects which need to beremoved. However, there are many instruments which have separateillumination and detection “arms” were detection and illuminationdepolarizers may be placed. For example, a quasi-normal-incidencereflectometer has slight offset illumination and detection beams. Mostellipsometers are other examples. For such instruments, it is sufficientto use two Lyot depolarizers, one in the illumination arm and one in thedetection arm, which have thicknesses that allow suitable averaging ofthe sum and difference frequencies. For example, if the four plates inthe two Lyot depolarizers have thickness ratios of 1:2:4:8, i.e., oneLyot depolarizer four times as thick as the other, the lowest frequencywill be simply that of the thinnest plate.

Many other embodiments are possible. For example, the plates can berotated by various angles, or stacked in various orders. While theinteger ratio of the thicknesses implied are preferable, other,non-integer ratios are possible. The three plates should preferably beof the same material so that f_(o) can be simultaneously maximized forall wavelengths (i.e. adjusting the design to increase f_(o) at onewavelength will not cause f_(o) to decrease at other wavelengths), butthe plates could possibly comprise different materials.

In addition to the use of a depolarizer, other techniques to minimizepolarization, particularly in the imaging path, can include componentpairing with perpendicular tilt planes and the use of spectrometers withpolarization scrambling optical fibers. The depolarizer's main role isin ensuring depolarized illumination of the sample, and to depolarizethe diffracted light from the sample before it interacts with anypolarization sensitive components in the imaging path of the system.

1. A method of optically inspection a sample comprising the steps of:generating a light beam; focusing the light beam onto the surface of thesample; collecting light reflected from the sample surface; monitoringthe reflected light with a spectrometer and generating output signals asa function of wavelength which can be used to analyze the sample; andcausing the light to pass through an image preserving polarizationscrambling element prior to being monitored, said element comprising athree plate depolarizer.
 2. A method as recited in claim 1, wherein eachof the plates is formed from a birefringent material.
 3. A method asrecited in claim 2, wherein the thicknesses of the plates are in theratio of 1:3:9.
 4. A method as recited in claim 2, wherein thethicknesses of the plates are in the ratio of 3:4:9.
 5. A method asrecited in claim 1, wherein the light beam includes visible and UVlight.
 6. A method as recited in claim 1, wherein the light beam isfocused and collected through the same microscope objective and thelight beam is directed to the sample with normal incidence.
 7. A methodas recited in claim 6, wherein said polarization scrambling element islocated on the side of the objective opposite to the sample.
 8. A methodas recited in claim 1, further including the step of eliminatingwavelength dependent perturbations in the output signals that are due tosaid polarization-scrambling element.
 9. A method of opticallyinspection a sample comprising the steps of: generating a light beam;focusing the light beam onto the surface of the sample; collecting lightreflected from the sample surface; monitoring the reflected light with aspectrometer and generating output signals as a function of wavelengthwhich can be used to analyze the sample; and causing the light to passthrough an image preserving polarization scrambling element either priorto being focused or after being collected and before being monitored.10. A method as recited in claim 9, wherein the element is located inthe path of the beam prior to being focused.
 11. A method as recited inclaim 9, wherein the element is located in the path of the beam afterbeing collected.
 12. A method as recited in claim 9, wherein the elementcomprises a birefringent plate depolarizer of two or more plates.
 13. Amethod as recited in claim 12, wherein said birefringent platedepolarizer comprises a Lyot depolarizer.
 14. A method as recited inclaim 12, wherein said birefringent plate depolarizer comprises athree-plate depolarizer.
 15. A method as recited in claim 14, whereinthe thicknesses of the plates are in the ratio of 1:3:9.
 16. A method asrecited in claim 14, wherein the thicknesses of the plates are in theratio of 3:4:9.
 17. A method as recited in claim 14, wherein all theplates have substantially different rotation angles of their ordinaryaxis.
 18. A method as recited in claim 9, wherein the light beamincludes visible and UV light.
 19. A method as recited in claim 9,wherein the light beam is focused and collected through the samemicroscope objective and the light beam is directed to the sample withnormal incidence.
 20. A method as recited in claim 19, wherein thepolarization scrambling element is a birefringent three platedepolarizer located on the side of the objective opposite to the sample.21. A method as recited in claim 9, further including the step ofeliminating wavelength dependent perturbations in the output signalsthat are due to said polarization-scrambling element.